What Researchers Learned from 350,757 Coin Flips

[@AnotherRoof]

To try everything Brilliant has to offer-free-for a full 30 days, visit brilliant.org/AnotherRoof You’ll also get 20% off an annual premium subscription. ⬣ *CORRECTIONS, CLARIFICATIONS, AND COMMON COMMENTS* ⬣ SURVEY forms.office.com/r/Hn63FACjGC 1. 18:45 a remark about the Bayesian argument used in [1]. This methodology aims to not only prove that the probability of the coin toss is greater than 0.5, but provide evidence for the fact that the probability is 0.508 as predicted by Diaconis et al. in [4]. Explaining this in detail is beyond the scope of this video, where I merely wanted to present convincing reasons why the coin tosses collected likely had p > 0.5. 2. At 12:12 I say "520 out of 1000" but the caption says "out of 100". Sorry! 3. There is a typo at 17:20. It's 350,757 flips, not 350,737. I checked those numbers *so many times* so can't believe I didn't spot that >_

[@warvinn]

Another typo at 12:12 unless you have some sort of hydra coin :D

[@AnotherRoof]

@@warvinn Well spotted! I'll add that now.

[@Martykun36]

"this year's Ig Nobel prize awarded to this flipping paper"

[@nolanhartwick7184]

The 'fair coin flip' method I was taught is to have both participants simultaneously flip a coin, with each player choosing matches/mismatches instead of heads/tails. Even if both players are cheating and using one sided coins or whatever, unless they have knowledge of how the other will cheat, it still ends up being 50:50 in practice.

[@dianapennepacker6854]

That is a failure of measurement! There will always be bias! Question is... How many decimals does it take. Why don't they make a perfect flipping machine in a vacuum to do the flipping. Do two sets. One starting heads. One starting tails. A million flips total or a piece. Coin used are changed to brand new ones every 1,000 flips. The flipping machine has to mimic a human thumb, and arm. Good luck making a perfect repeatable machine to do that. Seriously no one has made a flipping machine? Surely a gambler has to try to get some advantage.

[@frantisekbartos9857]

Great video! Thanks for covering our paper and reaching out with the questions!

[@Imperial_Squid]

Thanks for helping out towards such vital research! Out of curiosity, were you a stable tosser or a wobbly tosser in the end?

[@frantisekbartos9857]

@@Imperial_Squid a bit wobbly, 50.5% with 10,148/20,100 same sides

[@yaksher]

@12:30 It's worth noting that this is a very common but _completely incorrect_ interpretation of p-values. Imagine a circumstance where we have 10000 coins. One is magically rigged to always land on heads, and the rest are fair, and they're otherwise indistinguishable and mixed uniformly together. You pick a coin and flip it 10 times and it lands on all heads. The probability that the coin you picked is rigged is just ~0.1, not ~0.999 (which is 1 minus the "p-value" here for rejecting the null-hypothesis that "the coin you picked is fair") (I am rounding 1024 to 1000 and also rounding 1/9999 to 1/10000 and I think maybe doing some other rounding). A result with a given p-value is _some updated to your belief about the likelihood._ The p-value tells you how much to update it by (so we got from 1 in 10000 odds of the null-hypothesis being false to 1 in 10 odds, a 1000x improvement from our p-value of 0.001), but if the thing being tested is astronomically unlikely to begin with, this hardly lets you be confident. Of course, in this case, we know exactly the prior probability of the null-hypothesis, which isn't usually true, making interpreting p-values in the real world much harder. But in general, when you see a study with a p-value of 0.05, the correct interpretation is not "this is true with probability 95%", it's *"this is 20 times more likely to be true than I thought it was."* If the study is "some random food cures cancer"... well, there's a whole lot of foods and most of them probably don't cure cancer. Footnote: the easy way to do the math here is in terms of odds. We started with 1:9999 odds of rigged:fair. The p-value of 1/1024 tells us that we have an odds-ratio of 1/p = 1024. This tells us that we have 1024:9999 posterior odds of a rigged coin. (This is exactly equivalent to Bayes theorem, where you would have P(rigged | 10 heads) = P(10 heads | rigged) * P(rigged) / P(10 heads) = P(10 heads | rigged) * P(rigged) / (P(10 heads | rigged) * P(rigged) + P(10 heads | fair) * P(fair)) = 1 * 0.0001 / (1 * 0.0001 + 1/1024 * 0.9999) = 1024/(9999 + 1024)

[@ckq]

14:00 They said 250,000 = 500² since. With that many flips the standard deviation is 50%/500 = 0.1% which is sufficient to differentiate 50% and 50.3%

[@warvinn]

Felt confident in my flipping skills, left the survey going HHHHHHTTTT I'm a fraud 😭

[@crsmith6226]

Before watching this I’m going to guess that the actual physical construction of the coin will matter quite a bit. A US Quarter may be weighted slightly to one side as compared to a Pound Sterling or Penny Edit: not even ten minutes in and I was wrong lol

[@fluffsquirrel]

I am excited for this project! I contributed in good faith (had to redo a few because of bounces, but I tried my best to keep it as consistent and honest as possible). Good luck on this interesting endeavor!

[@Geenimetsuri]

Euro 20 cent: 8 heads, 2 tails. All started as heads. Started with flipping 5 heads in a row. Low height flips, but two did roll to floor, both heads.

[@litigioussociety4249]

In America houses usually start with 100 on one side, and 101 on the other, so your example doesn't work everywhere, and the fact is not always true.

[@o_enamuel]

1:28 loved the sheet!

[@paulsidhuUK]

Looking forward to the Premier but can predict if you did an odd number of flips its not 50/50 😉

[@Kounomura]

With so many throws, it can happen that the coin falls on the edge and stays there. Of course, it depends on how the throw is made.

[@paulsidhuUK]

@@Kounomura that's true. Landing on its edge would also make it not 50/50 as there are now 3 states: head, tails and edge. So the paradigm 50/50 is actually invalid. Good point.

[@Autumn_username]

Well the more coins you flip, the less likely it becomes for the results to be exactly 50/50 (only considering even numbers of flips because it’s impossible for odd numbers). But as it gets less likely for it to be exactly 50/50, it becomes more likely for it to be arbitrarily close to 50/50 as a proportion of the total number of coins thrown. Not close to 50/50 in terms of by how many flips off it is. I’m pretty sure. I might be wrong.

[@SomeTomfoolery]

Was thinking the exact same thing! 😂

[@TheDReeve1]

Tails never fails

[@peppermann]

Another fantastic video, many thanks 😎👍🏻

[@adamjohnson2117]

Stats is not my thing either but You have outlined alpha which guards against a false positive. Perhaps they did a power calculation (beta probably 0.8). This would calculate how big n has to be in order to detect a true positive (guards against false negatives)

[@blue2003fordwindstar]

3:26 "in twenty o seven" stealing this

[@Kounomura]

I think that the more times we throw, the number of absolute differences between heads and tails will increase, but the ratio of differences to all throws will become smaller and smaller.

[@canaDavid1]

Is it possible to fake toss the other side, by somehow hitting the coin with two different impulses at slightly different times? Like, starting it out normally but rehitting it after half a turn to stop it in its rotation?

[@not_David]

1:23 minutes in an my mind is already blown

[@Qermaq]

What these researchers need to understand is that if you do 27 trials you cannot have a 50-50 split. You gotta do an even number for it to ever work. :D

[@Kounomura]

I think we would get a strange result if e.g. we would toss 1 billion times, because in the meantime the coin would slowly wear, deform and not necessarily evenly.

[@Kounomura]

I would also be interested in whether it is possible to make a precision machine that can regularly throw heads and tails in a pre-defined ratio. In theory, if all parameters, all circumstances are the same, then the result should be the same. The question is whether "all conditions" can be technically implemented. The ordinary concept of probability is strongly related to not knowing something or making small mistakes. At the same time, it is very difficult to imagine the "objective chance" without a cause.

[@bencheevers6693]

It is so hard to deliver the exact same impulse over and over again, especially over a large enough sample size, like as a thought experiment it's perfectly doable, but the physical reality of building an apparatus which is going to deteriorate ever so slightly over use, the batteries will lose charge, the grid will wobble ever so slightly at peak times. If you look at those robots that throw the coin the same way every time they only flip over a couple times so the noise gets lost but in a real flip that rings and the coins flipping so quickly, I think it would be a hell of an engineering challenge. What I mean is any method of storing the same amount of energy will decay, whether it's springs or capacitors, the micro controller will read differently over time, the pad that launches the coin will wear, all these physical systems aren't tunable or able to be measured back to perfect over a million flips, there are so many different facets that would need to be controlled and kept exactly the same. I've noticed with a big silver coin, I can flip it from the same side and interrupt it with timing intentionally and get a better than 50/50 chance at calling it right, like doing 5 in a row, losing the timing, picking it up again and doing 6 or 7 more, I've gotten something like 30 heads to 10 tails before and I'm sure I could get better at it if I practiced but that 1 oz silver coin rotates slowly compared to a quarter but it's cool because even a real flip that looks impressive and rings is controllable. I think that's the only way to control a coin toss, trying to get a quarter to spin quickly and control it's landing without intentionally catching it at a certain timing in sync with it's rotation while you already know which side you started on is really difficult.

[@agustinzarzur]

I am from argentina and i love your videos and i did the survey and when i did it at first but i got way to many tails in my flips so then i did it again because there where some bounces so i did it again with the less error posible i still got that 7/10 of my flips where tails, maybe it's because of the coin i used (25 cents), where the heads is heavier so it could be that, i'm not sure

[@Novastar.SaberCombat]

People got PAID to do this. 🙄 After outlining, writing, editing, formatting, designing, and publishing 600,000 words and 350+ non-A.I. illustrations, do ya think *I* could get paid a decent amount?!? "No."

[@SomeTomfoolery]

Starting side Heads up Heads - 4 Tails - 6

[@FrugalHoser]

As for house numbers.... I think you forgot about zero... isn't that even? So equal chance addresses are odd or even right?

[@AnotherRoof]

Never seen a house 0 in my 32 years in this planet!

[@thenobody_]

They are flipping into their own hand, right? There is probably a nonzero chance a coin will land on it's edge if flipped onto a flat surface.

[@hcesarcastro]

I would like an experiment to help me get higher rolls in my d20.

[@noThankyou-g5c]

all i want to know is if any of the flips resulted in a tie (landing on its side)

[@QazaqCode]

Ofc its not. Start impulse, rotation resistance, bits by bits add up. 😅

[@TopRob1]

I got 9/10 same sided throws, it was clean and i submitted my results, I swear it's not rigged, I even repeated the experiment and got 5/10, it's just a coincidence

[@muskyoxes]

The average coin flipper, and especially NFL referees, are extremely bad at it. The coin flips like four or fewer total times

[@chuckles3265]

You can't start with a cat and then later dispense with it as unnecessary, that's just bad science.

[@estebanembroglio6371]

two are dice, one is a die!

[@angelowentzler9961]

This one is going to turn some heads (or tails)

[@Nickrioblanco1]

The only thing I understood was the terrible pun! 🤪

[@alh-xj6gt]

my ten time and started with head: hththttth

[@JonJones-pz9kb]

yes nice

[@timgutteridge5330]

In real situations some people catch the flipped coin and report the result. Some catch the flipped coin then place it (the other way up) on the back of their other hand and report that result. Is this discrepancy addressed in the experiment?

[@clemdelaclem]

Math has brought this man to the point where he spent all of his youtube money to go to the bank to ask for a copious amounts of coins as set dressing

[@-Kerstin]

Tl;dr people that can't flip a coin does not produce a coinflip. Pretty useless

[@blueskytoday2230]

Tom Stoppard had the answer, kzbin.info/www/bejne/aYqreXt7nJicpcU or not.

[@EpicGamerScout]

Shame to see another otherwise good video with the random annoying background music

[@jessehammer123]

I factored 350757- it’s 3^3*11*1181. My best guess would have been that they had 99 people each flip 3543 times. Why 3543? Dunno. Why 99? Maybe they wanted 100 but one had to drop out at the last minute.

[@GellyGelbertson]

the video explains there are 50 flippers with varying counts of flips attributed. it's likely the number is more arbitrary than so planned

[@stapuft]

No, its closer to 49\49\1 than 50\50, as there is less than 1% of a chance for ot to pand on its edge. Which is EXACTLY anqlagous to gender\sex and is why we compare the two when talking about "binary 'choices' "

[@soyanshumohapatra]

*Tails>>>>>>Heads* I know that already